Overview
This lecture explains how to identify and correctly use significant figures (sig figs) in measurements and calculations to reflect the precision of scientific data.
Understanding Significant Figures
- Significant figures are all certain digits in a measurement plus the first uncertain digit.
- The last digit reported in a measurement is always estimated.
- Zeros can be significant or just placeholders, depending on their position in the number.
Rules for Identifying Significant Figures
- All nonzero digits are significant.
- Captive zeros (between nonzero digits) are significant.
- Leading zeros (before all nonzero digits in decimals) are not significant.
- Trailing zeros are significant only if the number contains a decimal point.
- Scientific notation clearly shows the number of significant figures.
Examples of Significant Figures
- 6,798,000 has 4 significant figures (if no decimal is shown).
- 6,000,798 has 7 significant figures.
- 6,000,798.00 has 9 significant figures.
- 0.0006798 has 4 significant figures.
Significant Figures in Calculations
- For addition/subtraction: result should have sig figs to the rightmost column that all terms share.
- For multiplication/division: result must have as many sig figs as the input with the fewest sig figs.
- When rounding, round up if the first dropped digit is 5 or higher; otherwise, do not round up.
Using Scientific Notation
- Scientific notation makes the number of significant figures explicit.
- Example: 450 (2 sig figs) = 4.5 × 10²; 450.0 (4 sig figs) = 4.500 × 10².
Key Terms & Definitions
- Significant figures (sig figs) — all certain digits and the first uncertain digit in a measurement.
- Captive zeros — zeros between nonzero digits; always significant.
- Leading zeros — zeros before all nonzero digits in decimals; not significant.
- Trailing zeros — zeros at the end; significant only with a decimal point.
- Scientific notation — a way to write numbers showing all significant figures clearly.
Action Items / Next Steps
- Practice identifying significant figures in various numbers.
- Complete skill-building and concept review exercises on significant figures and calculations.
- Apply significant figure rules when reporting calculations on assignments.